Mass Transfer Effects: Immobilized and Heterogeneous Reaction Systems - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 894

0.93108 g/m 3 : Eqn (E17-4.4) gives K b ¼ Now if we assume C AS ¼ 2.148; f ¼ 8.700; Eqn

(E17-4.7) gives h 1 ¼ 0.11054; Eqn (17.47b) gives h 0 ¼ 0.1120; Eqn (17.64) gives h ¼ 0.11078.

0.91318 g/m 3 , which is slightly different from our first calculated

Eqn (E17-4.9) gives C AS ¼

value.
To get a converged solution, we use Excel solver continuing on the iterations (toward C AS
not changing), we obtain C AS ¼ 0.91349 g/m 3 , h ¼ 0.11036. This solution is very close to that

from our second iteration.
Eqns (E17-4.1) and (E17-4.2) gives

V ¼ Q C A0 C Ab
r A

C A0 C Ab C A0 C Ab

¼ Q

ðr AS ÞV gel =V ¼ Q

(E17-4.10)

r max C AS
ðK m þ C AS Þ ð1 ε Þ

h

h

Thus,

C A0 C Ab

¼ 100

50 1
0:11036 0:4 0:91249

m 3 V ¼ Q

3600

r max C AS
ðK m þ C AS Þ ð1 ε Þ

h

2 þ 0:91249 0:2

m 3 ¼ 491:7

The required working volume of the reactor is 491.7 m 3 .

17.6. ENCAPSULATION IMMOBILIZATION

When enzymes or other biocatalysts are immobilized via encapsulation, there is no reac-
tion occurring outside of the “porous particle.” A schematic of the geometry is shown in
Fig. 17.9 . Substrate is transferred from the bulk fluid phase to the outer shell (external
surface) of the particle and then permeates through the shell, reaching the biocatalyst.
That is,

at inner surface ¼ðr Ai Þ

k p
d S S O ðC Ai C AS Þ¼D eA S

d C A
d x

k c S O ðC Ab C Ai Þ¼ h (17.81)

where S O is the surface area of the outer shell, k p is the permeability of A through the
capsule shell, d S is the thickness of the capsule shell, C Ai is the concentration of the A at
the outer surface (interface), and C AS is the concentration of A at the inner shell surface
of the capsule.
There are three parameters one can control, in addition to the particle size. These param-
eters are: enzyme of biocatalyst loading (inside the capsule), capsule shell material, or perme-
ability and the capsule shell thickness. When permeability k p is increased and/or the shell
thickness is decreased, mass transfer rate increases and thus favorable to the reaction system
as whole, However, there is a limitation on the capsule shell material: containing the bio-
catalyst inside the shell while sustaining the reaction environment. Therefore, the capsule
shell is physically limiting the reaction system. Particle size effect follows the same trend
as solid catalyzed systems: smaller particle size leads to higher mass transfer rate and higher
effectiveness factor.